Related papers: Virtual Manifolds and Localization
With rapid advancements in the area of mobile robotics and industrial automation, a growing need has arisen towards accurate navigation and localization of moving objects. Camera based motion estimation is one such technique which is…
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
Despite the number of works published in recent years, vehicle localization remains an open, challenging problem. While map-based localization and SLAM algorithms are getting better and better, they remain a single point of failure in…
Localization is an essential capability for mobile robots. A rapidly growing field of research in this area is Visual Place Recognition (VPR), which is the ability to recognize previously seen places in the world based solely on images.…
In this work, we aim to improve the 3D reasoning ability of Transformers in multi-view 3D human pose estimation. Recent works have focused on end-to-end learning-based transformer designs, which struggle to resolve geometric information…
To fill the lack of research efforts in virtual assembly of modules and training, this paper presents a virtual manipulation of building objects in an Immersive Virtual Environment (IVE). A worker wearing a Virtual Reality (VR) head-mounted…
Monocular visual odometry (VO) is an important task in robotics and computer vision. Thus far, how to build accurate and robust monocular VO systems that can work well in diverse scenarios remains largely unsolved. In this paper, we propose…
Accurate localization in diverse environments is a fundamental challenge in computer vision and robotics. The task involves determining a sensor's precise position and orientation, typically a camera, within a given space. Traditional…
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
The existence of interesting multiplicative cohomology theories for orbifolds was first suggested by string theorists. Orbifold products have been intensely studied by mathematicians for the last fifteen years. In this paper we focus on the…
We introduce the notion of a topological geodesic in a 3-manifold. Under suitable hypotheses on the fundamental group, for instance word-hyperbolicity, topological geodesics are shown to have the useful properties of, and play the same role…
Robust robot localization is an important prerequisite for navigation, but it becomes challenging when the map and robot measurements are obtained from different sensors. Prior methods are often tailored to specific environments, relying on…
Visual localization is a core component in many applications, including augmented reality (AR). Localization algorithms compute the camera pose of a query image w.r.t. a scene representation, which is typically built from images. This often…
We investigate the performance of algebraic multigrid methods for the solution of the linear system of equations arising from a Virtual Element discretization. We provide numerical experiments on very general polygonal meshes for a model…
Omics software tools have reshaped the landscape of modern biology and become an essential component of biomedical research. The increasing dependence of biomedical scientists on these powerful tools creates a need for easier installation…
In many safety-critical applications such as autonomous driving and surgical robots, it is desirable to obtain prediction uncertainties from object detection modules to help support safe decision-making. Specifically, such modules need to…
We introduce a non-associative model for the Hilbert scheme of points in arbitrary dimension. We define a smooth ambient space, which we call the non-associative Hilbert scheme, containing the classical nested Hilbert scheme…